Owhadi H. Kernel Mode Decomposition and the Programming of Kernels 2021

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Owhadi H. Kernel Mode Decomposition and the Programming of Kernels 2021

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Textbook in PDF format This monograph demonstrates a new approach to the classical mode decomposition problem through nonlinear regression models, which achieve near-machine precision in the recovery of the modes. The presentation includes a review of generalized additive models, additive kernels/Gaussian processes, generalized Tikhonov regularization, empirical mode decomposition, and Synchrosqueezing, which are all related to and generalizable under the proposed framework. Although kernel methods have strong theoretical foundations, they require the prior selection of a good kernel. While the usual approach to this kernel selection problem is hyperparameter tuning, the objective of this monograph is to present an alternative (programming) approach to the kernel selection problem while using mode decomposition as a prototypical pattern recognition problem. In this approach, kernels are programmed for the task at hand through the programming of interpretable regression networks in the contextof additive Gaussian processes. It is suitable for engineers, computer scientists, mathematicians, and students in these fields working on kernel methods, pattern recognition, and mode decomposition problems. Preface Acknowledgments Introduction Review The Mode Decomposition Problem Kernel Mode Decomposition Networks (KMDNets) Additional Programming Modules and Squeezing Non-trigonometric Waveform and Iterated KMD Unknown Base Waveforms Crossing Frequencies, Vanishing Modes, and Noise Appendix Bibliography Index